What is a Mechanical Theorem Prover?

A mechanical theorem prover is a computer program that finds
proofs of theorems.

The ideal mechanical theorem prover is automatic: you give
it a formula and it gives you a proof of that formula or tells you
there is no proof.

Unfortunately, automatic theorem provers can be built only for very
simple logics (e.g., propositional calculus) and even then
practical considerations (e.g., how many
centuries you are willing to wait) limit the problems they can solve.